Annual Total Returns [BarChart] - First Trust Materials AlphaDEX Fund - First Trust Materials AlphaDEX Fund	Dec. 01, 2020
Bar Chart Table:
2010	28.15%
2011	(10.11%)
2012	25.11%
2013	26.73%
2014	(0.98%)
2015	(9.83%)
2016	29.17%
2017	23.68%
2018	(22.55%)
2019	21.54%

If the Fund has annual returns for at least one calendar year, provide a bar chart showing the Fund's annual total returns for each of the last 10 calendar years (or for the life of the Fund if less than 10 years), but only for periods subsequent to the effective date of the Fund's registration statement. Present the corresponding numerical return adjacent to each bar. If the Fund's fiscal year is other than a calendar year, include the year-to-date return information as of the end of the most recent quarter in a footnote to the bar chart. Following the bar chart, disclose the Fund's highest and lowest return for a quarter during the 10 years or other period of the bar chart. When a Multiple Class Fund offers more than one Class in the prospectus, provide annual total returns in the bar chart for only one of those Classes. The Fund can select which Class to include (e.g., the oldest Class, the Class with the greatest net assets).

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 4
-Subsection b
-Paragraph 2
-Subparagraph ii

+ Details

Name:	rr_AnnualReturn2010
Namespace Prefix:	rr_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 4
-Subsection b
-Paragraph 2
-Subparagraph instructions
-Clause 3
-Exhibit a

+ Details

Name:	rr_AnnualReturn2011
Namespace Prefix:	rr_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 4
-Subsection b
-Paragraph 2
-Subparagraph ii

+ Details

Name:	rr_AnnualReturn2012
Namespace Prefix:	rr_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 4
-Subsection b
-Paragraph 2
-Subparagraph ii

+ Details

Name:	rr_AnnualReturn2013
Namespace Prefix:	rr_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 4
-Subsection b
-Paragraph 2
-Subparagraph ii

+ Details

Name:	rr_AnnualReturn2014
Namespace Prefix:	rr_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 4
-Subsection b
-Paragraph 2
-Subparagraph ii

+ Details

Name:	rr_AnnualReturn2015
Namespace Prefix:	rr_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 4
-Subsection b
-Paragraph 2
-Subparagraph ii

+ Details

Name:	rr_AnnualReturn2016
Namespace Prefix:	rr_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 4
-Subsection b
-Paragraph 2
-Subparagraph ii

+ Details

Name:	rr_AnnualReturn2017
Namespace Prefix:	rr_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 4
-Subsection b
-Paragraph 2
-Subparagraph ii

+ Details

Name:	rr_AnnualReturn2018
Namespace Prefix:	rr_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form
-Number N-1A
-Chapter A
-Section 4
-Subsection b
-Paragraph 2
-Subparagraph ii

+ Details

Name:	rr_AnnualReturn2019
Namespace Prefix:	rr_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

Name:	rr_BarChartTableAbstract
Namespace Prefix:	rr_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	dei_LegalEntityAxis=ftetaf_S000017702Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	rr_ProspectusShareClassAxis=ftetaf_C000048902Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: